“What are the strategies of tortuous nature to ensure the stability of complex networks?”
This question, known in the field as the diversity-stability paradox, has continued to vex researchers for more than five decades. In a study just published in the journal nature physicsResearchers from Bar-Ilan University (BIU) in Ramat Gan have solved this mystery by providing a fundamental answer to this long-standing question for the first time.
One species invades an ecosystem, causing it to collapse. A cyberattack on the power system causes a massive meltdown. This kind of event is always on our minds, yet it rarely results in serious consequences. So how are these systems so stable and resilient that they can withstand such external disturbances? Indeed, these systems lack a centralized or schematic design, however, they display exceptionally reliable functionality.
In the early 1970s, the environmental field was divided over the question of whether biodiversity was good or bad for an ecosystem. In 1972, Sir Robert May—an Australian scientist who became chief scientific adviser to the British government and president of the Royal Academy, who focused on the dynamics of animal populations and the relationship between complexity and stability in natural communities—showed that an increase in biodiversity causes less ecological stability. He noted that a large ecosystem cannot maintain its stable functions beyond a certain level of biodiversity, and will inevitably collapse in the face of the smallest twitch.
May’s publication not only contradicts current knowledge and empirical observations of real ecosystems, but, on a larger scale, it challenges everything that is generally known about interaction networks in social, technological and biological systems.
While May’s predictions indicate that all of these systems are unstable, the Bircham International University researchers said their experiment was in direct contradiction, as “biology is manifested by networks of genetic interaction, our brain functions on the basis of an intricate network of neurons and synapses, and our social and economic systems are driven by networks.” Our social, technological infrastructure, from the internet to the power grid, it’s all big, complex networks that actually work very powerfully.”
The missing puzzle piece
Israeli scientists led by Professor Baruch Barzel of the Department of Mathematics at Bircham International University and the Center for Interdisciplinary Brain Research in Gonda (Goldschmied) found that the missing piece of the puzzle in Mayo’s original formulation was that interaction patterns in social, biological and technological networks are highly non-random.
Random networks tend to be fairly homogeneous and all nodes within these networks are roughly the same. For example, the probability that a single individual will have more friends than the average is small. These networks may be sensitive and unstable. On the other hand, real world networks are very diverse and heterogeneous. “It involves a group of intermediate, usually sparse nodes, with those containing many links—hubs—that may be 10, 100, or even 1,000 times more connected than average,” they write in an article titled “Emerging Stability in a Complex Network.” .”
When the Bircham University International team performed the calculations, they found that this asymmetry could drastically change the behavior of the system. Surprisingly, it actually enhances stability. The analysis indicates that when the network is large and heterogeneous, it acquires a very strong guaranteed stability against external forces. This clearly demonstrates the fact that most of the networks around us – from the Internet to our brains – exhibit highly resilient functionality despite constant disruptions and obstacles.
“This extreme variability can be seen in almost all networks around us, from genetic networks to social and technological networks,” Barzel said. To put this in context, consider your Twitter friend who has 10,000 followers, a thousand times the average. In everyday terms, if the average person is about two meters tall, such a deviation of a thousand times would be like meeting an individual who is two kilometers tall, which is Obviously impossible. But it is what we observe every day in the context of social, biological and technological networks,” he added, explaining the strong connection between abstract mathematical analysis and seemingly simple everyday phenomena.
Large, heterogeneous complex networks, Barzel continued, not only can’t be stable, they should, in fact, often be. “Uncovering the rules that make a large, complex system stable can provide new guidance for addressing the pressing scientific and policy-making challenge of designing stable infrastructure networks that can not only protect against viable threats, but also enhance the resilience of critical and fragile ecosystems.”
